Introduction to Abstract Mathematics

This information is for the 2019/20 session.

Teacher responsible

Dr Peter Allen and Prof Konrad Swanepoel


This course is compulsory on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.


Students should have taken, or be taking concurrently, the course Mathematical Methods (MA100).

Course content

The course is an introduction to the use of formal definitions and proofs in mathematics, and to basic results of elementary set theory, number theory, linear algebra, algebra and analysis. Specific topics covered are as follows: Logic, integers, sets and functions, prime numbers, relations, real and complex numbers, greatest common divisor and modular arithmetic, infimum and supremum, sequences, limits, continuity, groups and vector spaces.


20 hours of lectures, 20 hours of classes and 10 hours of workshops in the MT. 21 hours of lectures, 20 hours of classes and 10 hours of workshops in the LT. 2 hours of lectures in the ST.

Formative coursework

Written answers to set problems will be expected on a weekly basis.

Indicative reading

Students may wish to have one of the recommended textbooks: N L Biggs, Discrete Mathematics (2nd edn) or P J Eccles, An Introduction to Mathematical Reasoning, but these are not required. Further background reading can be found in R Allenby, Numbers and Proofs; M Liebeck, A Concise Introduction to Pure Mathematics; V Bryant, Yet Another Introduction to Analysis; R Bartle & D Sherbert, Introduction to Real Analysis and H Anton, Elementary Linear Algebra.


Exam (100%, duration: 3 hours) in the summer exam period.

Key facts

Department: Mathematics

Total students 2018/19: 238

Average class size 2018/19: 14

Capped 2018/19: No

Value: One Unit

Guidelines for interpreting course guide information

Personal development skills